Algebra Formulas Sheet

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For solving problems by applying different principles or properties of algebra, we need different formulas. These formulas help us reach to the solution of the problem efficiently and effectively. Algebra Formulas Sheet is used for solving certain complicated problems. Following are the certain formulas that we use in Algebra formulas: -

1.    a^2-b^2 = (a+b) (a-b)

2.    (a+b) ^2 = a^2 + 2ab + b^2

3.    (a-b) ^2 = a^2 -2ab + b^2

4.    a+b = b+a [ Commutative property]

5.    a + (b+c) = (a+b) +c [Associative Property]

6.    a(b+c) = ab + ac [Distributive Property]

7.    A + 0 = a [ Identity Property]

8.    a * 0 = 0 [Zero Property]

9.    FOIL method – (m + n) (x + y) = mn + my + nx + ny

10. Equation of any line with slope m and the y intercept b is given as y = mx + b

11. Equation of line with slope m and one of the co-ordinates lying on the line as (x1, y1) is (y-y1) = m (x-x1)

Let us take some examples where we can apply the Algebra formulas from the sheet.
 
Example 1: - Expand (3x+4y) ^2

Solution: -Given equation is:-

(3x+4y) ^2

We know that (a+b) ^2 = a^2 + 2ab + b^2

We get 9x^2 + 24xy + 16y^2

Example 2:  Factorize 4y^2 – 36z^2

Solution:-

Given equation is:-

4y^2 – 36z^2

= (2y) ^2 – (6z) ^2

= (2y + 6z) (2y – 6z)    [ a^2 – b^2 = (a + b) (a – b)]

Hence the solution is (2y + 6z) (2y – 6z).
 
 
 
 

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